MATM48 Fourier Analysis, 7.5 credits, is an elective course for a Master of Science degree in mathematics. The course can be taken as an stand-alone course. The course is given at half-study pace during the second half of the spring semester. The language of instruction is English. MATM48 replaces previous editions of the course Fourier Analysis with the course codes MATM38 and MATM18.

Course Content
The course treats L¹ and L²theory of Fourier series and integrals, pointwise convergence and summation methods (with respect to "good" kernels) of Fourier series and integrals, the finite Fourier transform, including the Fast Fourier transform algorithm, examples of applications in physics and in other areas of mathematics, such as dynamical systems, number theory, uncertainty principles, harmonic analysis and partial differential equations.

Teaching
The teaching consists of lectures and seminars. Homework assignments are included in the course.

Assessment
The examination consists of a written examination and a corresponding oral examination at the end of the course. The oral examination is only given to those students who have passed the written examination. Completed homework assignments and presentation of solutions to exercises in the seminars can give a certain amount of bonus points; this will be specified at the start of the course.

Course Literature

E.M.Stein, R.Shakarchi, Fourier analysis, Princeton Lectures in Analysis I, Princeton University Press, 2003.
Dym H., McKean H. P., Fourier Series and Integrals, Academic Press, New York, 1972.
Katznelson Y., An Introduction to Harmonic Analysis, third edition, Cambridge Math. Lib., Cambridge Univ. Press, Cambridge, 2004

Official Course Description

Course Evaluation
Link to course evaluations on the department's website:

Course Evaluations, Mathematics at Faculty of Science